# Baryogenesis and helical magnetogenesis from the electroweak transition of the minimal Standard Model

## TL;DR

This paper investigates how the electroweak transition in the Standard Model can produce baryon asymmetry and helical magnetic fields through sphaleron dynamics, CP violation, and related phenomena.

## Contribution

It introduces the concept of sphaleron freezeout, analyzes CP violation during sphaleron explosions, and estimates the baryon asymmetry generated within the Standard Model.

## Key findings

- Sphaleron production rates depend on size and phase of the universe.
- CP violation peaks at sphaleron freezeout temperature around 130 GeV.
- Estimated CP violation is an order of magnitude below what's needed for observed baryon asymmetry.

## Abstract

We start by considering the production rates of sphalerons with different size $\rho$ in the symmetric phase, $T>T_{EW}$. At small $\rho$, the distribution is cut off by the growing mass $M\sim 1/\rho$, and at large $\rho$ by the magnetic screening mass. In the broken phase, $T<T_{EW}$ the scale is set by the Higgs VEV $v(T)$. We introduce the concept of "Sphaleron freezeout" whereby the sphaleron production rate matches the Hubble Universe expansion rate. At freezeout the sphalerons are out of equilibrium. Sphaleron explosions generate sound and even gravity waves, when nonzero Weinberg angle make them non-spherical. We revisit CP violation during the sphaleron explosions. We assess its magnitude using the Standard Model CKM quark matrix, first for nonzero and then zero Dirac eigenstates. We find that its magnitude is maximal at the sphaleron freezeout condition with $T\approx 130\, GeV$. We proceed to estimate the amount of CP violation needed to generate the observed magnitude of baryon asymmetry of Universe. The result is about an order of magnitude below our CKM-based estimates. We also relate the baryon asymmetry to the generation of $U(1)$ magnetic chirality, which is expected to be conserved and perhaps visible in polarized intergalactic magnetic fields.